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Suppose that I have several boards. Four of them are 2 inches long, three of them are 3 inches long. How many ways are there to combine them to make 11 inches? Or to make 7 inches? I need the formula that allows me to enter the lengths of various boards, the number of each size, and the total length of the combination.

R McFadin
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    Welcome to the Math Stack Exchange! This looks like an interesting question, but this site has some standards which your question appears to not satisfy; i.e. Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress (what have you tried so far?), why the question is interesting or important, etc. – Vepir Aug 20 '20 at 16:58
  • Say the total length is $n$, that $x_1,x_2,\dots,x_i,\dots$ are sizes of available boards and that $t_1,t_2,\dots,t_i,\dots$ are the amounts of available boards. Are you asking what is the number of partitions of $n$ such that summand $x_i$ appears at most $t_i$ times, for the given sets of boards? – Vepir Aug 20 '20 at 17:04
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    Do you consider the boards to be the same? For example, for the question "how many ways are there to make a combination of length 2 inches", is the answer 1 or 4? – Matti P. Aug 21 '20 at 07:39
  • In general, this looks like finding the number of integer solutions to $$ 2x_1 + 3x_2 = n $$ with some limitations on how large $x_1$ and $x_2$ can be . – Matti P. Aug 21 '20 at 07:41

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